PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Binet-Cauchy Kernels on Dynamical Systems and its Application to the Analysis of Dynamic Scenes
S V N Vishwanathan, Alex Smola and Rene Vidal
International Journal of Computer Vision 2005.


We derive a family of kernels on dynamical systems by applying the Binet-Cauchy theorem to trajectories of states. Our derivation provides a unifying framework for all kernels on dynamical systems currently used in machine learning, including kernels derived from the behavioral framework, diffusion processes, marginalized kernels, kernels on graphs, and the kernels on sets arising from the subspace angle approach. In the case of linear time-invariant systems, we derive explicit formulae for computing the proposed Binet-Cauchy kernels by solving Sylvester equations, and relate the proposed kernels to existing kernels based on cepstrum coefficients and subspace angles. Besides their theoretical appeal, these kernels can be used efficiently in the comparison of video sequences of dynamic scenes that can be modeled as the output of a linear time-invariant dynamical system. One advantage of our kernels is that they take the initial conditions of the dynamical systems into account. As a first example, we use our kernels to compare video sequences of dynamic textures. As a second example, we apply our kernels to the problem of clustering short clips of a movie. Experimental evidence shows superior performance of our kernels.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2044
Deposited By:S V N Vishwanathan
Deposited On:16 January 2006